Practical Handbook of Curve Design and Generation

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Computers are now being used virtually everywhere in arts, drafting, and design to generate curves and surfaces ranging from the elementary to the intricate. Practical Handbook of Curve Design and Generation is a ready reference that presents the basic mathematics of curves in a complete, clear manner that enables you to apply the material to your own work with minimum effort. By knowing how curves are mathematically generated and how their shape is controlled, you can more fully exploit available computer tools, modify these tools themselves, and provide input for others to modify them. It will also help you to identify mathematical equations required to produce specific curves. The book does not require a heavy mathematical background-if you understand elementary algebra and trigonometry, you can fully apply the material presented. Essential mathematical concepts are repeated in the book to reinforce your knowledge of those topics.
Featuring some 300 graphic examples, the book is organized so that early chapters cover fundamental polynomial, trigonometric, and exponential forms. The mathematical transformation of curves is then treated in order to give you a general approach for modifying known curves. Later chapters introduce complex curves that can be composed from the building blocks presented in earlier chapters. The final chapters cover interesting ideas in space curves and in surfaces.

Publisher ‏ : ‎ CRC Press; 1st edition (8 March 1994)
Language ‏ : ‎ English
Hardcover ‏ : ‎ 288 pages
ISBN-10 ‏ : ‎ 084938916X
ISBN-13 ‏ : ‎ 978-0849389160
Item Weight ‏ : ‎ 226 g
Dimensions ‏ : ‎ 17.15 x 2.54 x 24.77 cm
Country of Origin ‏ : ‎ India

Reviewer: John A. Bauer
Rating: 5.0 out of 5 stars
Title:
Review: The chapters of this book go further in-depth into various classes of curves than any source material I have seen elsewhere. For example, the chapter on Lissajous curves covers several variations you get zero results for when web searching. The section on hypo & epi trochoids (aka Spirograph) is extremely thorough, with several examples I have seen in mathematical art which made me think “Oh, that’s how they draw that!” There is a good chapter on deformations which can be applied in many situations, along with a gentle introduction to some polynomial approximations of the curves.No book is without its imperfections. In this case, perhaps a little more exploration of some more advanced math behind these curves would be welcome. However, I do recognize that exploring the calculus governing a lot of these shapes would have made the book significantly longer and perhaps not added too much to the overall quality of the book. There are one or two mathematical errors, but an astute reader will catch on to them readily enough. More relevant might have been some practical uses of the various curves, or an explanation of where some of them show up in nature or in natural phenomenon. For example, a Lissajous curve is the pattern a compound pendulum traces, which would be a nice fact to include in the book.Although there is perhaps little practical value in knowing how to produce a “compound harmonic Lissajous curve”, this book has rarely left my side over the past few months as I used it to produce a wide variety of novel marble run pieces compatible with my children’s marble run toys. At the very least, I can provide another answer for what you can do with a compound harmonic Lissajous curve: you can make a nice butterfly shaped marble run piece.

5

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